Parametrization and Approximation Methods in Feedback Theory with Applications in High-gain, Fast-sampling, and Cheap-optimal Control

Many high performance feedback control design problems can be parametrized by plant or control parameters such as sampling rates, controller gain, or control weighting in linear quadratic-optimal control. The paper describes a general input-output framework for a unified description of many such problems which permits the designer to use simple approximate plant models to achieve stabilization and desired performance characteristics from the real plant by off-line design based on the use of the approximate model. The analysis uses a judicious mix of asymptotic analysis and functional analytic methods and is applied to high-gain, fast-sampling, and cheap-optimal control based on first-order plant models.